Finite Group Databasebeta

← #10943976

Subgroups — #10943976

Order 768.

2008 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#459C211yesmaximal, characteristic, complemented
3C2×#5156C212yesmaximal, complemented
4#83192C211yesmaximal, characteristic, complemented
5C2×#5072C211yesmaximal, characteristic, complemented
6#72037C212yesmaximal, complemented
7#71604C211yesmaximal, characteristic, complemented
8#70479C211yesmaximal, characteristic, complemented
9#70475C211yesmaximal, characteristic, complemented
10#70208C212yesmaximal, complemented
11#70200C212yesmaximal, complemented
12#32902—31nomaximal, Sylow
13C22×D3×D4C2211yescharacteristic
14C23×C4×D3—21no—
15C22×C3×D8C2212yes—
16C2×C3×#127C2211yescharacteristic, complemented
17C2×C3×C4×D4C2211yescharacteristic
18C2×#938—21no—
19C2×#938—21no—
20C2×#938C2212yes—
21C2×D4×Dic3C2211yescharacteristic
22C22×#213C2212yes—
23C2×C4×#67—21no—
24C4×D3×D4—24no—
25C4×D3×D4—24no—
26C2×#893C2211yescharacteristic
27C2×D3×C4⋊C4C2211yescharacteristic
28C2×#67⋊C4—21no—
29C2×D3×C22⋊C4—21no—
30C2×C4×D12C2211yescharacteristic
31C2×C42×D3C2211yescharacteristic
32C3×#459—24no—
33C2×C3×C4⋊C8C2211yescharacteristic, complemented
34C2×C3×#102C2212yescomplemented
35#5221—21no—
36#5221—21no—
37#5221C2212yescomplemented
38C2×#832C2212yes—
39C2×#832C2212yescomplemented
40#5156—28no—
41C2×#821C2212yes—
42C2×(C2×D3)⋊C8C2212yes—
43#5072—24no—
44#4935C2211yescharacteristic, complemented
45C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
46#4551C2212yescomplemented
47#4550C2212yescomplemented
48#4529C2212yescomplemented
49C22×C4×D4—31no—
50C2×#459—31no—
51C2×#459D311yescharacteristic, complemented
52C2×#447—32no—
53#2856—31no—
54#1879—32no—
55#1879—32no—
56#1874—32no—
57#1802—31no—
58#1802—31no—
59#1797—31no—
60C24×D3—21no—
61C22×C3×D4—21no—
62C22×C3×D4—21no—
63C22×C3×D4C2312yes—
64C22×C3×D4C2311yescharacteristic
65C23×C3×C4—21no—
66C22×#67—22no—
67C22×#67—21no—
68C23×Dic3—21no—
69C2×D3×D4—22no—
70C2×D3×D4—22no—
71C2×D3×D4—22no—
72C2×D3×D4—22no—
73C2×D3×D4—22no—
74C2×D3×D4D414yescomplemented
75C22×D12C2311yescharacteristic
76C22×C4×D3—28no—
77C22×C4×D3—21no—
78C22×C4×D3—21no—
79C22×C4×D3—21no—
80C22×C4×D3—44no—
81C22×C4×D3—44no—
82C22×C4×D3D411yescharacteristic
83C22×C4×D3D411yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C2×C3×D8—24no—
86C2×C3×D8—24no—
87C2×C3×D8—24no—
88C22×C3×C8C2312yes—
89C3×#127—22no—
90C3×#127—22no—
91C3×C4×D4—22no—
92C3×C4×D4D414yescomplemented
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C22⋊C4—21no—
95C2×C3×C42C2311yescharacteristic
96C2×#217—21no—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—22no—
100#938—24no—
101#938—24no—
102#938—44no—
103#938—44no—
104D4×Dic3—22no—
105D4×Dic3—22no—
106C2×#213—24no—
107C2×#213—24no—
108C2×#213—24no—
109C4×#67—28no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3—21no—
114C2×C4⋊Dic3C2312yes—
115C2×C4⋊Dic3C2311yescharacteristic
116C2×Dic3⋊C4—21no—
117C2×C4×Dic3D411yescharacteristic
118C2×C4×Dic3D411yescharacteristic
119C2×C4×Dic3C2311yescharacteristic
120C22×C3⋊C8C2312yes—
121#893—22no—
122#893—22no—
123D3×C4⋊C4—22no—
124D3×C4⋊C4—22no—
125#67⋊C4—28no—
126D3×C22⋊C4—28no—
127C4×D12—22no—
128C4×D12D414yescomplemented
129C42×D3—22no—
130C42×D3—22no—
131C3×C4⋊C8—22no—
132C3×#102—24no—
133#832—24no—
134#832—24no—
135#821—24no—
136(C2×D3)⋊C8—24no—
137C4⋊(C3⋊C8)—22no—
138C23×D4—31no—
139C24×C4—61no—
140C22×D8—32no—
141C22×D8C2×D312yes—
142C2×#127C2×D311yescharacteristic, complemented
143C2×#121—32no—
144C2×#121—61no—
145C2×#121—61no—
146C2×C4×D4—31no—
147C2×C4×D4—31no—
148C2×C4×D4—31no—
149C2×C4×D4—61no—
150C2×C4×D4—61no—
151C2×C4×D4—64no—
152C2×C4×D4—64no—
153C2×C4×D4C2×D311yescharacteristic
154C22×C4⋊C4—31no—
155C22×C22⋊C4—61no—
156C22×C42—31no—
157#459—24no—
158#459—64no—
159#447—68no—
160C2×C4⋊C8—31no—
161C2×C4⋊C8C2×D311yescharacteristic, complemented
162C2×#102—32no—
163C2×#102—32no—
164C2×#102—32no—
165C2×#102C2×D312yescomplemented
166C2×C22⋊C8—32no—
167#390—32no—
168#390—61no—
169#390—61no—
170#384—31no—
171#340—32no—
172#340—32no—
173#336—32no—
174C24×C3—21no—
175C24×C3—22no—
176C23×D3—24no—
177C23×D3—24no—
178C23×D3—21no—
179C23×D3—24no—
180C23×D3—42no—
181C23×D3—42no—
182C23×D3—42no—
183C23×D3—42no—
184C23×D3C2×D411yescharacteristic
185C2×C3×D4—21no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—42no—
195C2×C3×D4—42no—
196C2×C3×D4—42no—
197C2×C3×D4—42no—
198C2×C3×D4—42no—
199C2×C3×D4—42no—
200C2×C3×D4C2×D412yes—
201C2×C3×D4C2×D412yes—
202C2×C3×D4#4112yes—
203C22×C3×C4—21no—
204C22×C3×C4—24no—
205C22×C3×C4—42no—
206C22×C3×C4—42no—
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2411yescharacteristic
210C2×#67—24no—
211C2×#67—24no—
212C2×#67—24no—
213C2×#67—44no—
214C2×#67—44no—
215C2×#67—44no—
216C22×Dic3—24no—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—42no—
220C22×Dic3—42no—
221C22×Dic3C2×D411yescharacteristic
222C22×Dic3C2×D411yescharacteristic
223C22×Dic3C2×D411yescharacteristic
224D3×D4—28no—
225D3×D4—28no—
226D3×D4—28no—
227D3×D4—28no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12C2×D412yes—
232C2×D12C2×D412yes—
233C2×D12#4112yes—
234C2×C4×D3—22no—
235C2×C4×D3—22no—
236C2×C4×D3—21no—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—24no—
241C2×C4×D3—24no—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—24no—
245C2×C4×D3—432no—
246C2×C4×D3—41no—
247C2×C4×D3—42no—
248C2×C4×D3—42no—
249C2×C4×D3—42no—
250C2×C4×D3—42no—
251C2×C4×D3—42no—
252C2×C4×D3—42no—
253C2×C4×D3D814yescomplemented
254C2×C4×D3C2×D412yes—
255C2×C4×D3#4112yes—
256C3×D8—48no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4C2×D412yes—
262C3×C22⋊C4—24no—
263C3×C42C2×D412yes—
264C3×C42C2×D412yes—
265#217—24no—
266#217—44no—
267#217—44no—
268#217—44no—
269#213—48no—
270(C2×D3)⋊C4—24no—
271(C2×D3)⋊C4—24no—
272C4⋊Dic3—21no—
273C4⋊Dic3—22no—
274C4⋊Dic3—22no—
275C4⋊Dic3—42no—
276C4⋊Dic3—42no—
277C4⋊Dic3C2×D412yes—
278Dic3⋊C4—24no—
279C4×Dic3—22no—
280C4×Dic3—22no—
281C4×Dic3—21no—
282C4×Dic3—21no—
283C2×C3⋊C8—22no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—22no—
286C25—61no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—34no—
290C22×D4—31no—
291C22×D4—62no—
292C22×D4—61no—
293C22×D4—62no—
294C22×D4—62no—
295C22×D4—62no—
296C22×D4—62no—
297C22×D4—62no—
298C22×D4C22×D312yes—
299C22×D4C22×D311yescharacteristic
300C23×C4—21no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—31no—
304C23×C4—61no—
305C23×C4—61no—
306C23×C4—68no—
307C23×C4—61no—
308C23×C4—61no—
309C23×C4—124no—
310C23×C4—124no—
311C2×D8—24no—
312C2×D8—24no—
313C2×D8—24no—
314C2×D8—64no—
315C2×D8—64no—
316C2×D8—64no—
317C22×C8—32no—
318C22×C8C22×D312yes—
319#127—22no—
320#127—22no—
321#121—64no—
322#121—64no—
323#121—124no—
324#121—124no—
325C4×D4—22no—
326C4×D4—34no—
327C4×D4—68no—
328C4×D4—62no—
329C4×D4—62no—
330C4×D4—68no—
331C4×D4—62no—
332C4×D4—62no—
333C4×D4—62no—
334C4×D4#6714yescomplemented
335C2×C4⋊C4—31no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—61no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—61no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4C22×D311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—68no—
345C2×C22⋊C4—61no—
346C2×C22⋊C4—61no—
347C2×C22⋊C4—61no—
348C2×C22⋊C4—62no—
349C2×C22⋊C4—62no—
350C2×C22⋊C4—62no—
351C2×C42—31no—
352C2×C42—31no—
353C2×C42—31no—
354C2×C42—62no—
355C2×C42—62no—
356C2×C42C22×D311yescharacteristic
357C4⋊C8—22no—
358C4⋊C8—62no—
359#102—24no—
360#102—64no—
361#102—64no—
362#102—64no—
363C22⋊C8—64no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3C22×D411yescharacteristic
379C22×D3—21no—
380C22×D3—21no—
381C22×D3—21no—
382C22×D3—21no—
383C22×D3—216no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—48no—
388C22×D3—48no—
389C22×D3—48no—
390C22×D3—48no—
391C22×D3—48no—
392C22×D3—41no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—48no—
397C22×D3#12112yes—
398C22×D3C2×D812yes—
399C22×D3AGL(1,ℤ/8)12yes—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4—22no—
403C3×D4—42no—
404C3×D4—42no—
405C3×D4—42no—
406C3×D4—42no—
407C3×D4—84no—
408C3×D4—84no—
409C3×D4#12114yescomplemented
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—48no—
416C2×C3×C4#12012yes—
417C2×C3×C4#12012yes—
418C2×C3×C4C2×D812yes—
419C2×C3×C4AGL(1,ℤ/8)12yes—
420C2×C3×C4C22×D411yescharacteristic
421C2×C3×C4C22×D411yescharacteristic
422C2×C3×C4C22×D411yescharacteristic
423C2×C3×C4C2×#4111yescharacteristic
424C2×C3×C4C2×#4111yescharacteristic
425C2×C3×C4C2×#4111yescharacteristic
426#67—216no—
427#67—88no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—22no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—48no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3#12112yes—
443C2×Dic3C2×D812yes—
444D12—22no—
445D12—22no—
446D12—22no—
447D12#12114yescomplemented
448C4×D3—22no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—28no—
453C4×D3—48no—
454C4×D3—44no—
455C4×D3—48no—
456C4×D3—48no—
457C3×C8—42no—
458C3⋊C8—42no—
459C24—21no—
460C24—22no—
461C24—31no—
462C24—64no—
463C24—64no—
464C24—64no—
465C24—61no—
466C24—122no—
467C24—122no—
468C24—122no—
469C24—122no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—32no—
480C2×D4—32no—
481C2×D4—32no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—64no—
489C2×D4—68no—
490C2×D4—68no—
491C2×D4—68no—
492C2×D4—64no—
493C2×D4—64no—
494C2×D4—68no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—124no—
499C2×D4—124no—
500C2×D4—124no—
501C2×D4D3×D412yes—
502C2×D4#23712yes—
503C2×D4C2×#6712yes—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—34no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—31no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—62no—
515C22×C4—64no—
516C22×C4—64no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—64no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—64no—
527C22×C4—62no—
528C22×C4—121no—
529C22×C4—122no—
530C22×C4—122no—
531C22×C4—122no—
532C22×C4—1232no—
533C22×C4—122no—
534C22×C4—122no—
535C22×C4—122no—
536C22×C4—122no—
537C22×C4—122no—
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4C23×D311yescharacteristic
541D8—48no—
542D8—128no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—62no—
547C2×C8—62no—
548C2×C8—62no—
549C4⋊C4—21no—
550C4⋊C4—32no—
551C4⋊C4—64no—
552C4⋊C4—61no—
553C4⋊C4—62no—
554C4⋊C4—62no—
555C4⋊C4—122no—
556C4⋊C4—122no—
557C4⋊C4C2×#6712yes—
558C22⋊C4—24no—
559C22⋊C4—64no—
560C22⋊C4—64no—
561C22⋊C4—64no—
562C22⋊C4—124no—
563C22⋊C4—124no—
564C22⋊C4—124no—
565C42—62no—
566C42—62no—
567C42—61no—
568C42—61no—
569C42D3×D412yes—
570C42C2×#6712yes—
571C22×C3—24no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3—82no—
584C22×C3—82no—
585C22×C3C2×#12011yescharacteristic
586C22×C3C2×#12111yescharacteristic
587C22×C3#52511yescharacteristic
588C22×C3C22×D811yescharacteristic
589C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
590C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
591C22×C3#57511yescharacteristic
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—24no—
599C2×D3—432no—
600C2×D3—42no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3#45914yescomplemented
607C3×C4—22no—
608C3×C4—42no—
609C3×C4#44714yescomplemented
610C3×C4C2×#12111yescharacteristic
611C3×C4C2×#12111yescharacteristic
612C3×C4#52511yescharacteristic
613C3×C4#52511yescharacteristic
614Dic3—22no—
615Dic3—22no—
616Dic3—42no—
617Dic3—41no—
618Dic3—82no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—32no—
623C23—32no—
624C23—32no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—616no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—128no—
645C23—128no—
646C23—128no—
647C23—128no—
648C23—128no—
649C23—128no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23C2×D3×D411yescharacteristic
655D4—22no—
656D4—22no—
657D4—22no—
658D4—34no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—616no—
664D4—62no—
665D4—62no—
666D4—62no—
667D4—84no—
668D4—84no—
669D4—248no—
670D4#93814yescomplemented
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—48no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—68no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—124no—
693C2×C4—128no—
694C2×C4—128no—
695C2×C4—128no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—128no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4D3×D812yes—
703C2×C4#91112yes—
704C2×C4#93712yes—
705C2×C4#93712yes—
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4C2×#23711yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C2×C4C22×#6711yescharacteristic
712C8—42no—
713C8—122no—
714C2×C3—44no—
715C2×C3—162no—
716C2×C3#284711yescharacteristic
717C2×C3C2×#44711yescharacteristic
718C2×C3#300611yescharacteristic
719C2×C3C2×#45911yescharacteristic
720C2×C3#303611yescharacteristic
721C2×C3#310011yescharacteristic
722C2×C3#310911yescharacteristic
723D3—24no—
724D3—44no—
725C22—24no—
726C22—34no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—62no—
734C22—62no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—64no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—1232no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—122no—
753C22—122no—
754C22D3×#12111yescharacteristic
755C22#560611yescharacteristic
756C22C2×D3×D811yescharacteristic
757C22C2×#91111yescharacteristic
758C22D3×AGL(1,ℤ/8)11yescharacteristic
759C22#577311yescharacteristic
760C22C2×#93711yescharacteristic
761C4—22no—
762C4—42no—
763C4—62no—
764C4—62no—
765C4—122no—
766C4—121no—
767C4—242no—
768C4#515614yescomplemented
769C4D3×#12111yescharacteristic
770C4#560611yescharacteristic
771C4C2×#93811yescharacteristic
772C4#582811yescharacteristic
773C3#3290211yescharacteristic, complemented, Sylow
774C2—44no—
775C2—64no—
776C2—124no—
777C2—162no—
778C2#8031211yescharacteristic
779C2#8031411yescharacteristic
780C2D3×#45911yescharacteristic
781C2#8033211yescharacteristic
782C2#8272311yescharacteristic
783C2C2×#515611yescharacteristic
784C2#8394611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#459C2
socleC23×C3C22×D4
hypercenterC2×#459D3
hypocenterC3#32902
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
2. C2×C3×#459C2semidirect
3. C2×#5156C2semidirect
4. #83192C2semidirect
5. C2×#5072C2semidirect
6. #72037C2semidirect
7. #71604C2semidirect
8. #70479C2semidirect
9. #70475C2semidirect
10. #70208C2semidirect
11. #70200C2semidirect
16. C2×C3×#127C22semidirect
33. C2×C3×C4⋊C8C22semidirect
34. C2×C3×#102C22semidirect
37. #5221C22semidirect
39. C2×#832C22semidirect
44. #4935C22semidirect
45. C2×C4⋊(C3⋊C8)C22semidirect
46. #4551C22semidirect
47. #4550C22semidirect
48. #4529C22semidirect
51. C2×#459D3semidirect
74. C2×D3×D4D4semidirect
92. C3×C4×D4D4semidirect
128. C4×D12D4semidirect
142. C2×#127C2×D3semidirect
161. C2×C4⋊C8C2×D3semidirect
165. C2×#102C2×D3semidirect
253. C2×C4×D3D8semidirect
334. C4×D4#67semidirect
409. C3×D4#121semidirect
447. D12#121semidirect
606. C2×D3#459semidirect
609. C3×C4#447semidirect
670. D4#938semidirect
768. C4#5156semidirect
773. C3#32902semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×D3×D42
C2×C3×#4592
C2×#51562
#831922
C2×#50722
#720372
#716042
#704792
#704752
#702082
#702002
#329023